# Tagged Questions

Invariance of a physical system (its action) under a continuous group of local transformations underlain by a global symmetry whose group parameters fixed in space-time have now been extended to vary in space-time instead. Use for buildup of the invariance, fixing the gauge, and accounting for the ...

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### When can a global symmetry be gauged?

Take a classical field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be ...
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### Why does charge conservation due to gauge symmetry only hold on-shell?

While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
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### Noether's theorem and gauge symmetry

I'm confused about Noether's theorem applied to gauge symmetry. Say we have $$\mathcal L=-\frac14F_{ab}F^{ab}.$$ Then it's invariant under $A_a\rightarrow A_a+\partial_a\Lambda.$ But can I say that ...
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### To which extent is general relativity a gauge theory?

In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
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### Invariance of Functional Integration Measure

Let us consider the functional integral: $$\int \mathcal{D} A e^{iS[A]}$$ where $S[A]$ is the action for $U(1)$ gauge field and \mathcal{D}A\equiv \...
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### Gauge invariant but not gauge covariant regularization

I'm not sure if someone's already asked this before, but I was wondering, in field theory, when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In ...
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### Gauge fixing and degrees of freedom

Today, my friend (@Will) posed a very intriguing question - Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions ...
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### Faddeev Popov Gauge Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
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### Gauge fields in Polyakov's treatment of renormalization for nonlinear sigma model

I am deriving the results of renormalization for nonlinear sigma model using Polyakov approach. I am closely following chapter 2 of Polyakov's book--- Gauge fields and strings''. Action for the ...
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### Intuition for gauge parallel transport (Wilson loops)

I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport". I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
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### Why mass terms are forbidden?

I would like to clarify my understanding on why mass terms in Lagrangians of gauge theories are forbidden. It's often repeated that particle masses are forbidden by electroweak symmetry because it is ...
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### Request for Reference: BRST formalism/transformations

Could anyone please suggest a very basic paper/reference/literature on BRST symmetry/formalism that requires rudimentary knowledge of Dirac's method for dealing with constrained systems and generation ...
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### Why does local gauge invariance suggest renormalizability?

I'm reading Gauge Field Theories: An Introduction with Applications by Mike Guidry and this particular remark is not obvious to me: A tempting avenue is suggested by the QED paradigm, for if a ...
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### Connection beween infinite gauge symmetries and UV finiteness

In e.g., http://arxiv.org/abs/arXiv:0712.3526 the author claims: Since the massless higher-spin field theories involve infinite-dimensional gauge symmetries, one expects that such theories may be ...
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### Gauge invariance and Bohm-Aharonov effect

I am confused with the Bohm-Aharonov effect: though quantum mechanics is said to be gauge invariant, the presence of a solenoid imposes a gauge. I used to think that a phase shift did not change ...
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### Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
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### Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? Thanks!...